Many methods and devices have been developed for measuring and describing the visual appearance of objects. These methods and devices are useful in a variety of contexts. For example, measurements of the visual appearance of an object can reveal properties of any paints, pigments, specialty coatings, surface treatments, etc., that may be present on the object. Also, for example, measurements of the visual appearance of an object can be used to create computer models, set production tolerances, etc. It is known to use various devices to provide spectral measurements of a surface of an object. Existing devices, however, either produce results of limited detail or are exorbitant in cost, size, and the time necessary for measurements.
For example, it is known to use discrete multi-angle spectrometers that measure reflectance over a limited number of viewing and illumination directions. An example of such a device is the MA68 available from X-RITE. All of these devices, however, either consider a limited number of viewing directions (e.g., coplanar directions), or consider data derived from all viewing angles together, for example, by summing or averaging over all directions. As a result, known discrete multi-angle spectrometers provide results that do not reflect directional variations in surface appearance. Referring to the coatings industry, these results can be useful to measure some properties of surfaces including conventional paints, pigments, and coatings. They are not as useful, however, for measuring properties of surfaces having specialized paints, pigments, and other specialty coatings that have different appearances when viewed from different angles, such as those that appear today on cars, boats, currency, consumer plastics, cosmetics, etc. For example, limited sample multi-angle spectrometers are not as useful for measuring properties of interference coatings such as, for example, pearlescent automotive paints that appear one color {e.g., white) from one angle and a second color (e.g., pink) from another angle. They also typically do not provide detailed enough results to tie properties of a surface back to physical features of the surface, for example, due to coating formulation and/or application process factors.
Some of the shortcomings of known discrete multi-angle spectrometers are addressed by devices that measure the complete Bidirectional Reflectance Distribution Function (BRDF) of a surface, such as goniospectrophotometers and parousiameters. The complete BRDF generated by these devices provides a rich characterization of the scatter off of a surface as a function of illumination angle, viewing angle, wavelength and other variables. Both of the referenced devices for measuring BRDF, however, have significant drawbacks.
Goniospectrophotometers, such as the GCMS-4 Gonio-Spectro-Photometric Colorimeter available from MURAKAMI, measure the complete BRDF by scanning both illumination and detection angles, typically over a complete hemisphere. Although they can provide good results, the devices are extremely large and expensive. Also, it can take several hours to scan illumination and detection angles over a complete hemisphere, making real-time applications impossible. Parousiameters, such as the one described in U.S. Pat. No. 6,557,397 to Wademan, measure the complete BRDF by projecting a range of illumination and detection angles onto a hemispheric screen and imaging the screen using a camera. The error of these devices, however, is directly related to the size of the hemispherical screen, and the devices cannot acceptably measure samples with an area greater than 10% of their screen's area. As a result, parousiameters are often large and bulky. Also, slots in the screen, and the limited dynamic range of most high resolution cameras further limit the device. In addition, because both goniospectrophotometers and parousiameters measure illumination and viewing angles over a complete hemisphere, noise issues can become a significant factor.
Spectrophotometers are used for the measurement of objects to provide spectral reflectance data that is converted into tristimulus colorimetric results, which may then be used for communication and display. This data is also used in developing ink formulations, pigments, and dyes used in the coloring of products meant to replicate the appearance of a measured object. In many cases, other features of the objects to be measured complicate the measurement process, making it difficult to obtain repeatable results. The dimensions of Cesia and Spatiality may be used to describe these additional perceptual effects (the physical equivalent dimensions of periodic and aperiodic subsurface scatter, spatial roughness, and local slope variation). Texture, coarseness and sparkle are examples of types of Cesia and Spatiality that can alter the perceived color of an object under different types of illumination and are of interest in recreating and replicating an image/object, e.g., when simulating appearance on a computer screen and/or when developing a recipe or formulation for replicating an object's color or appearance.
Traditional methods of formulation and rendering do not accurately account for the noted effects and often simply ignore them. The net result is an inaccurate estimation of the true color of the object along with a failure to account for these effects. A simple example is a metallic automotive paint, where the addition of metal flakes provides a “sparkling” effect under directional illumination, and the perception of dimensional “coarseness” when viewed under diffuse illumination. Without the metallic flakes, the base diffuse color would appear darker. Addition of metallic flakes tends to lighten the apparent color of the object while simultaneously providing a sparkling effect. Additionally, process effects may cause the perceived lightening to change based on viewing and illumination angle. Furthermore, variations in flake size distribution may cause batch-to-batch variations that are perceptible, e.g., as color and/or sparkle differences, even though the nominal flake size remains constant.
Historically, spectrophotometers used to measure object color have typically involved a single illuminator and a single receiver configured in a 0/45 or 45/0 configuration (illumination angle/receiver angle relative to surface normal). However, due to the other perceptual dimensions of Cesia and Spatiality (physical equivalent dimensions of periodic and aperiodic subsurface scatter, spatial roughness and local slope variation), such instrumentation is unable to provide repeatable results for most common objects, particularly when such objects are rotated and/or moved about. Furthermore, renderings and formulations based on measurements made with conventional spectrophotometer instruments will yield inaccurate results except for the simplest of cases.
For most situations, the historical solution has involved either providing diffuse illumination or diffuse receiver (or both) by changing the optics or through the addition of an integrating sphere. However, sphere-based spectrophotometers tend to simply “average up” the results, integrating the goniometric and spatially-distributed changing color and lightness reflectance over a hemisphere so as to provide a single result. While this functionality helps to remove rotation- and translation-based measurement instability, it results in a single spectral curve that combines the Cesia and Spatiality effects with the color, resulting in an incorrect color result.
Multi-angle and scanning goniospectrophotometers overcome the foregoing limitations by providing multiple angles of illumination and receiving pickup. As a result, many spectral curves are generated that characterize the response of the sample under each illumination and observation (receiving) condition. Examples of such instruments include the Revolution system available from IsoColor Inc. (Carlstadt, N.J.), the SOC200 available from Surface Optics Corp (San Diego, Calif.), the BYK-MAC available from BYK-Gardner (Columbia, Md.), and the MA98 available from X-Rite, Inc. (Grand Rapids, Mich.). A challenge presented by these commercially available instruments is that they are able to generate a large number of spectral curve results in a very short time with only a few measurements. Even if the data is reduced to 3 dimensional color space results, there are still many different answers for a single measurement object, raising the question: Which result (illumination/observation angle) is the “single correct” color? Indeed, each result correctly represents the color of the object for a given set of illumination/observation conditions. In view of the above-noted challenge, current commercial instrumentations are not equipped to efficiently and effectively use spectral curve data, e.g., to provide an accurate rendering visualization on a computer screen and/or to develop a formulaic recipe.
Computer visualization shares many similarities to the development of a formulaic recipe for color replication. Both situations seek to simulate the response of light as it impinges on an object of given composition to generate a desired color response. Examples abound in the computer graphics literature and technical literature. Most commonly, an object's response to light is defined by the BRDF mathematical function referenced above. Of note, the BRDF function may be referenced in various ways, e.g., BSSRDF and BTF, depending on the specific implementation of the measurement configuration. Generally, each of the noted regimens are aimed at capturing how an object's illumination is modified and transformed by the object to generate its reflectance (and transmittance) in different directions.
In the simple case of a 0/45 spectrophotometer or an integrating sphere spectrophotometer, the fact that only a single spectral curve is generated for a single measurement has been addressed, e.g., in the computer graphics industry, through simplified mathematical reflectance lobe functions commonly known as Phong, Blinn-Phong, Cook Torrance, La Fortune, etc. These models assume that the single color measurement result is fundamentally correct and modify this base color to create common Cesia effects such as Gloss. However, the information required for modification is not typically available from the measurement and other knowledge about the object is required to correctly model and visualize the higher order effects, e.g., spatiality, and to accurately model Cesia effects. Furthermore, if the original object is glossy or features texture(s), then the single spectral curve measurement results will contain the contribution of these effects and, therefore, modeling of even the basic diffuse color will be inaccurate.
In the case of formulation, the problems are similar. Assuming only a single spectral curve, formulation software optimization models use a database of material properties to combine contribution of effects to create estimates of spectral response. These predicted results are compared to the measured (or desired) results and the error minimized through the use of merit functions. Common models include Kabelka Munk, Multiflux Phase, Effective Medium Theory, and other similar derivatives. The noted models share a great deal of similarity to the computer visualization models and, therefore, suffer many of the same deleterious effects. More particularly, the noted models utilize simple concepts of additive and subtractive color (absorption and reflection) as well as gross assumptions regarding subsurface scattering, and simple weighting functions to predict the spectral response of the material (or coating). This prediction is compared against the measured or desired results and the error difference minimized through iteration. Because the models are simplified and the single spectral curve contains the same assumptions and errors described above due to the inclusion of Cesia and Spatiality effects, the results are prone to error. Corrections are made to the models to account for gross assumptions, such as Fresnel Reflectance Coefficients and their relationship to the dielectric constants, but errors due to process effects giving rise to Cesia and Spatiality (e.g., agglomeration and orange peel in automotive paints) are not accounted for.
Indeed, conventional software is formulaic in nature, creating only a recipe of ingredients and amounts—there is little or no attempt to account for batch or production process induced variation in the formulation process. However, such process effects typically modify the Cesia and Spatiality of the object and therefore directly and/or indirectly affect the color of the object both physically and in the net measurement result (thus further inducing error in the optimization process).
With the introduction of multiangle and scanning goniospectrophotometers, more robust rendering and formulation software has been developed. Models such as the Multi Flux Phase (with additional terms), the Henyey Greenstein formalization, and the Fuzzy Logic methods of Osumi et al., allow for additional terms to modify the shape of the BRDF lobe from spherical or elliptical to higher order shapes depending on the number of terms involved. These models improve on the simple single spectral curve and assumed mathematical BRDF lobe functions described above. Although such modifications accommodate the optimization utilizing many spectral curves (as opposed to one), they do not attempt to utilize the information contained in the desired set of spectral curves to decompose process effects from formulation effects and recipe changes. There is no attempt made to classify potential ingredients other than traditional “n” and “k” (dielectric constant and scatter coefficients). As a result, they still suffer from the same inability to separate process induced Cesia and Spatiality changes from formulaic batch variability and recipe changes.
Thus, despite efforts to date, a need remains for a method of measuring an object's true color accounting for physical material-related properties, such as Cesia and Spatiality, derived from both batch variability and recipe changes. A need also remains for visualization and formulation of true color that incorporates the effects of both batch variability and recipe changes on physical material related properties. These and other needs are satisfied by the systems and methods disclosed herein.